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Most scientists don't think so.

The reason the question isn't patently ludicrous is that a) physics doesn't really say much about what's inside the event horizon of a black hole, and b) the radius of the event horizon scales directly with mass for black holes. So the larger a black hole is, the lower its average density is. Galactic-mass black holes can have surprisingly low densities (again: on average; at the singularity, density is infinite).

It turns out that if you plug a reasonable guess for the mass of the observable universe into the equation for the Schwarzhild radius of a black hole, you get a radius of ... approximately the radius of the observable universe. Within a couple of orders of magnitude, anyway (and in cosmology, that's considered pretty close). So it's not as silly a question as it might appear at first.

However, the reason we don't think the universe is inside a black hole is that a) the universe is expanding, which is hard to reconcile with it being inside a black hole, and b) it doesn't look like the universe has enough mass to halt the expansion (in fact, the expansion appears to be accelerating).

There are a few, however, who do think it's possible. For some reason adding related links is not working, but do a Google search for "national geographic universe black hole" and you should find a recent (Feb 2014) article about it.

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Q: Does this universe exist within a black hole?
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When will a black hole hit your universe?

There are already black holes within the universe


In what part is a black hole in the universe?

Astronomers believe that black holes exist in the center of every universe. They even think that there may be a black hole in the center of our galaxy, the Milky Way


Can you make a black hole inside a black hole?

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Does the black hole spaghettifie you?

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Does a black hole have billions of stars in it?

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Why cannot you believe that a black hole can be the centre of the universe?

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Is the universe a black hole so to speak?

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